Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 202800.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.bo1 | 202800dn4 | \([0, -1, 0, -2238968, -1284551568]\) | \(502270291349/1889568\) | \(4669738920198144000\) | \([2]\) | \(3686400\) | \(2.4416\) | |
| 202800.bo2 | 202800dn2 | \([0, -1, 0, -143368, 20939632]\) | \(131872229/18\) | \(44483871744000\) | \([2]\) | \(737280\) | \(1.6369\) | |
| 202800.bo3 | 202800dn3 | \([0, -1, 0, -75768, -38548368]\) | \(-19465109/248832\) | \(-614945042989056000\) | \([2]\) | \(1843200\) | \(2.0951\) | |
| 202800.bo4 | 202800dn1 | \([0, -1, 0, -8168, 389232]\) | \(-24389/12\) | \(-29655914496000\) | \([2]\) | \(368640\) | \(1.2903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 202800.bo do not have complex multiplication.Modular form 202800.2.a.bo
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
